It's the day after a 14 innning marathon where every guy in the bullpen plus Lincecum pitched as a closer in the 14th, and 2 days after a starter only went 3 innings. The bullpen was totally taxed. And the Giants have a day game tomorrow.
Bumgarner has only thrown 70 pitches through 7 shutout innings. And that includes sitting through an hour long rain delay in the 3rd inning. He could easily pitch into extra innings if it goes that far.
For the Phillies A.J. Burnett is starting the 7th inning having already thrown 110 pitches. I guess the Phillies don't want to go to their bullpen either.